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Stat 3011 (Geyer) Second Midterm (Computer Lab Part)

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General Instructions (Please Read!)

• For simple computer commands, you may write the command you used and the result it gave on this test form.
• For complicated commands or plots, make a printout and attach the printout to the test form (we'll provide a stapler).

Question 1 [20 pts.]

Suppose a random variable T has Student's t distribution with 5 degrees of freedom.

1. Find the probability that T is greater than 2.0.
2. Find the probability that T is greater than 10.0.
3. Find the probability that T is greater than 2.0 in absolute value, that is, pr(|T| > 2.0).
4. Find the t such that pr(T > t) = 0.15.
5. Find the t such that pr(|T| > t) = 0.15.

You may use the form below to answer this question.

If you want to print your results (not necessary, you can write the R commands you used on the test paper instead), replace "your name here" with your actual name in quotes.

Question 2 [20 pts.]

The file t2.dat contains a single variable named height consisting of measurements of height in centimeters of 15 students.

1. Draw some sort of plot that shows you the shape of the distribution of the data. Hand in this plot.
2. Make a 95% confidence interval for the true population mean, assuming the students are a random sample from some specified population.
3. Does your plot from part (a) tell you anything about whether this confidence interval is approximately valid? If so, what?
4. Make a 99% confidence interval for the true population mean, assuming the students are a random sample from some specified population.

You may use the form below to answer this question.

The form automatically loads this data set t2.dat (like the lecture section examples). You don't need to do anything to load the data.

Put your name on the plot before printing it. Either replace "your name here" with your actual name in quotes, or add the optional argument main="your name" to the plot command.

Question 3 [15 pts.]

Recalculate using the computer the confidence interval we did by hand yesterday about the arthritis trial. The entire question is repeated below.

A drug company has performed a randomized controlled trial of a new nonsteroidal anti-inflammatory drug for treatment of arthritis. The control group got an old drug (ibuprofen) and the treatment group got the new drug. There were 250 patients in each group. The patients were randomly assigned to treatment or control. Treatments were deemed "successful" if the patient reported "acceptable" or better quality of life. The results were

You may use the form below to answer this question.

If you want to print your results (not necessary, you can write the R commands you used on the test paper instead), replace "your name here" with your actual name in quotes.